Any triangle that maintains the proportional sides of 12:15:18 will be similar to triangle ABC. Examples include triangles with sides measuring 6cm, 7.5cm, 9cm or 24cm, 30cm, 36cm.
To determine which triangle is similar to triangle ABC with sides AB=12cm, BC=15cm, and AC=18cm, we need to find a triangle that has the same angle measurements.
Similar triangles have the same shape but may differ in size.
These triangles will have their corresponding sides proportional to one another.
To find such a triangle, we construct a triangle with sides that are multiples or fractions of 12, 15, and 18 while maintaining the same ratio.
For instance, a triangle with sides of 6cm (12/2), 7.5cm (15/2), and 9cm (18/2), has maintained the ratio of sides of triangle ABC and thus would be similar to it.
We can also use a multiple such as 2 to form a triangle with sides 24cm (12*2), 30cm (15*2), and 36cm (18*2) and it will still be similar to triangle ABC.
The core concept here is that the sides of similar triangles are proportional, and therefore any triangle that maintains the ratio of 12:15:18 will be similar to triangle ABC.
The probable question may be:
In triangle ABC, AB=12cm, BC= 15 cm and AC=18 cm.
Which triangle is similar to triangle ABC